The spectral expansion solution method is a technique for computing the stationary probability distribution of a continuous-time Markov chain. It is used to calculate the stationary probability distribution vector of a two-dimensional state space, where one dimension has a finite limit and the other is unbounded. The stationary distribution vector is expressed in terms of eigenvalues and eigenvectors of a matrix polynomial.

This course explores the role of randomness in computation and pseudorandomness, focusing on the applications in error-correcting codes, expander graphs, randomness extractors, and pseudo-random generators. The course will also address the question of derandomization of small-space computation. Prerequisites are unspecified, but the course content suggests a high level of expertise.